The idea of direct utility function U(X) is that as long as the quantity of various commodities purchased (consumed) by consumers is fixed (regardless of how other related economic variables (such as price vector P) are set or changed), consumers' preference or utility is unique. That is, the determined consumption beam x corresponds to the determined utility function value U(X).
The indirect utility function v(P, m) is based on the direct utility function U(X) and only takes the consumption bundle X as the independent variable. The idea is that as long as the commodity price vector P and the consumer budget constraint M are fixed, consumers will maximize the value of their direct utility function U(X) under the constraint of PX=m, and the maximum value of U(X) is the function value of the indirect utility function v(P, m). In particular, it should be pointed out that both the commodity price vector P and the consumer budget constraint M faced by consumers are certain, and the purchase and consumption bundle X that consumers maximize their utility level does not need to be uniquely determined (although it is uniquely determined most of the time), but the values of the direct utility function U(X) corresponding to these different vectors X must be unique "maxima".
From the definition of direct utility function U(X) and the process of establishing and solving indirect utility function v(P, m), we can find that the two utility functions are essentially the same. The indirect utility function v(P, m) is based on the direct utility function U(X). That is to say, whether it is the direct utility function U(X) or the indirect utility function v(P, M), as long as the quantity of goods consumed by consumers is certain, consumers will have a certain degree of utility. As for the direct utility function U(X), the independent variable x has a "direct decisive effect" on the dependent variable U(X), which is why U(X) is called the "direct utility function". For the indirect utility function v(P, m), the decisive role of independent variables p and m on the dependent variable-utility level must actually be completed through a certain number of bundles X (or a collection of bundles of goods) that consumers finally consume. Therefore, the independent variables P and M play an "indirect decisive role" in the dependent variable utility level. The solution process shows that the utility level is still directly determined by the consumption beam X, which is why v(P, m) is called "indirect utility function".
The diminishing marginal benefit is a basic concept of economics. It says that in an enterprise with resources as input, the utility of unit resource input to product output is decreasing. In other words, although its total output is increasing, its second reciprocal is negative, which slows down its growth rate, makes it eventually tend to peak and may decline.
The most obvious explanation is nonlinear function, such as conic.
In life, we can see many examples: I give you a lovely one, and you jump for joy, thinking that you have earned it, and then the second one … but if I keep giving it to you, you will feel sick. There are two reasons: first, you are full and don't need physiology; Second, you are tired of excitement. You want a chance to express yourself, "boss, give it to Hagen, okay?"
The so-called new official takes office with three fires, which is also the truth: when you are new here, you have to get acquainted, so you will do your best. Over time, it will fade. General textbooks will explain it like this: mysterious psychology and sociology.
If we establish a mapping that makes various utilities comparable (for example, we define that running fast is not as good as running steadily, which is not meaningless, and the racing industry is an example), then in a time series, both input and output (as well as cumulative input and cumulative output) can be used as models. As can be seen from the above two examples, this concept can be understood as two characteristics: first, t=0 is greater than t->; The output at infinity is much larger (this is an image of a sequence function). Second, t-> T and t->; T+ 1 at t->; There is little change at infinity (this is the first reciprocal of the image). The former shows that the overall trend is decreasing, while the latter shows that the rate of decrease is slowing down.
We can think about the law of diminishing marginal utility, which is universal. You are thinking about CET-4, so you find a valuable book, recite it from A, which is good, and it will be finished in a short time (of course, A is not much, so I am such a person), and then B, and then ... B Part 2, and then B Part 2 1/2 ... The concept of series is, of course, that you can choose to start from Z and go back (of course, I
It can be seen that input and output are the same concept, because input needs output, so the inverse of diminishing marginal benefits still applies.
We can expand to leave the concept of utility. Let's look at a practical problem:
I cleaned the room yesterday and found that there was a layer of dust on the table I just cleaned, which looked no different from a small bracket next to it. Actually, I wasn't in Nanjing the last time the latter had plastic surgery. ...
A thing rises quickly from clean to dirty, but it is a long process from dirty to dirty. Are you looking forward to the archaeological team? (although there are also evaluation factors)
You can also think of many things, for example, to be human, "what is lost is true."
How do we use this rule? The explanation of economics is the optimal allocation of resources. Because too much investment makes the final income spread too thin. There is a limit to the best things. Science and engineering know better that the so-called advanced operation is thankless to some extent, and the most effective operation is often the basic operation. More profound, of course, are some math games.
However, I think the origin of this phenomenon is definitely a philosophical issue, which is also the reason for our progress and development.
Think about it, if the marginal benefit is increasing, do we still need innovation? Do we still need to insist? Comrades, cuteness is enough, no, cold water will do! The word charm has lost its meaning forever.